ISIJ International
Online ISSN : 1347-5460
Print ISSN : 0915-1559
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Effect of Pearlite Structure on Lattice Strain in Ferrite Estimated by the Williamson-Hall Method
Yuki TanakaDaichi AkamaNobuo NakadaToshihiro TsuchiyamaSetsuo Takaki
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2015 Volume 55 Issue 11 Pages 2515-2517

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Abstract

The effect of pearlite on the X-ray diffraction peak reflected from ferrite phase in ferrite-pearlite steel was investigated using normalized carbon steels with different volume fraction of pearlite and a hypereutectoid steel with different interlamellar spacing. The lattice strain in ferrite phase, which causes the broadening of X-ray diffraction peak, was increased in proportion to both of the volume fraction of pearlite and the inverse of interlamellar spacing. As a result, the lattice strain in ferrite-pearlite steel can be simply formulated as a function of them. On the other hand, TEM observation reveals that pearlite has low-density dislocation in ferrite phase. This result suggests that the misfit between ferrite and cementite in pearlite generates the significant amount of elastic strain, which leads to the increase in lattice strain. Therefore, the dislocation density must be overestimated in carbon steels with pearlite, if it is estimated from the experimental lattice strain directly.

1. Introduction

It is generally known that the flow stress of metals is increased in proportion to the square root of dislocation density, which is called Bailey-Hirsch relationship.1) Authors estimated the dislocation density of cold-rolled ultralow carbon steel by means of Williamson-Hall method (W-H method)2) with X-ray diffractometry, and reported that the relation between dislocation density (ρ: m−2) and yield stress (σy: Pa) given by the Eq. (1) holds for the specimens cold-rolled up to 90% in reduction.3,4,5)   

σ y 10 8 +12 ρ (1)
The dislocation density estimated by W-H method almost agrees well with the results obtained by neutron diffractometry6) and TEM observation,7,8) and thus, the measurement using X-ray diffraction could be regarded to be a valid method for obtaining dislocation density of steels, at least ferritic single-structured iron. However, when the dislocation density of commercial low-carbon steels is measured by W-H method, the effect of pearlite structure should be taken into account.

Authors found that pearlite structure contains a significant degree of elastic strain which is due to lattice misfit between ferrite and cementite, and this causes a broadening of full width at half maximum (FWHM) of X-ray diffraction peaks.9,10,11) Since the W-H method estimates dislocation density from FWHM broadening by the lattice strain due to non-uniform deformation,12) it is possible that the dislocation density of ferrite in ferrite-pearlite steel might be overestimated if the FWHM detected is directly used with no consideration of elastic strain within the pearlite. In order to estimate dislocation density of ferrite-pearlite steel correctly, the effect of pearlite structure on the FWHM must be quantitatively evaluated and removed from the apparent dislocation density obtained from the detected FWHM.

In this study, the effect of pearlite on the X-ray diffraction peak reflected from ferrite phase in ferrite-pearlite steel was investigated using normalized carbon steels with different volume fraction of pearlite and a hypereutectoid steel with different interlamellar spacing, and then lattice strain of ferrite phase in ferrite-pearlite steel was formulated as functions of volume fraction of pearlite and interlamellar spacing.

2. Experimental Procedures

The materials used in this study were pure iron (0.0056 mass%C), S15CK (0.16 mass%C), S25C (0.23 mass%C), S45C (0.44 mass%C) and SK85 (0.89 mass%C) in order to change volume fraction of ferrite and pearlite. These steels were cold rolled by 50% reduction in thickness and then cut to the plates (20l×40w×2t mm). The steel plates were solution-treated at 1223 K for 1.8 ks followed by air-cooling at cooling rate of 4 K/s to normalize. Additionally, a commercial hypereutectoid steel with a chemical composition of Fe-0.9C-0.9Mn-0.4Si (mass%) was used. This steel was solution-treated at 1223 K for 1.8 ks and then subjected directly to isothermal holding at 823–973 K, followed by water-cooling to obtain fully pearlitic structure with different interlamellar spacing. Microstructure of the specimens were observed by optical microscopy, scanning electron microscopy (SEM) and transmission electron microscopy (TEM). Especially, the deeply etched area where cementite lamellar existed vertically to the observation surface was selectively observed to measure the average interlamellar spacing (L). For X-ray diffractometry (XRD), specimens were wet polished by sand paper and electrochemical polished to eliminate the surface layer strained by sand paper grinding. The XRD measurement was performed using a X-ray diffractometer equipped with a Cu-Kα radiation source (RINT2100 instrument developed by Rigaku Corp.). The observed diffraction peaks of ferrite phase were corrected by splitting into the peaks diffracted by Cu-Kα1 and Cu-Kα2 radiations after removing of the buck ground using the software program (PDXL2). After that, owing to quantify the lattice strain (ε), full width at half maximum (β) measured from the peaks at each diffraction angle (2θ) was plotted according to the following Williamson-Hall equation (W-H method).2)   

β cosθ λ = 0.9 D +2ε sinθ λ (2)
Here, λ and D are X-ray wavelength (Cu-Kα1, 0.154 nm) and crystallite size, respectively. In this analysis, (200)F diffraction was deselected owing to high anisotropy and the artifact that came from the equipment itself was removed using β for fully annealed interstitial atom free (IF) steel.13)

3. Results and Discussion

Figure 1 represents optical and scanning electron micrographs of normalized specimens. The volume fraction and interlamellar spacing of cementite in each specimen are also shown in the figures. The measured volume fraction of pearlite (VP) reasonably corresponds to the Fe–C binary equilibrium diagram, which means fully normalized standard structure has been formed with no significant overcooling during the normalizing. Here, the grain size of ferrite measured by the quadrature method were approximately 50 μm for pure iron and 10 μm for the others.

Fig. 1.

Optical micrograph and scanning electron micrograph of steels that were air-cooled from 1223 K. (a) Pure iron, (b) S15CK, (c) S25C, (d) S45C and (e) SK85. Vp and L mean volume fraction of pearlite and lamellar spacing, respectively.

As an example of X-ray diffraction peak profiles, Fig. 2 shows the (110)F peak profile. There is a tendency that the peak shifts toward lower angle and the FWHM broadens significantly with increasing volume fraction of pearlite. The peak shift toward lower angle means an expansion of lattice plane spacing, and this seems to be derived from an increase in lattice constant corresponding to the amount of solute carbon.14) However, it is hardly thought that the amount of solute carbon is different among the specimens because they have fully normalized standard structure. As other possibilities, partitioning of the alloying element of Mn and/or Cr, anisotropy of elastic strain in pearlite, and so on, should be considered, but it is hard to identify the main reason so far, and thus, we need more investigation in future. On the other hand, the broadening of FWHM would have been affected by the elastic strain within pearlite structure as mentioned in the Introduction. To clarify the effect of pearlite, the lattice strain of ferrite obtained by W-H method (the effect of crystallite size is removed15)) was plotted as a function of volume fraction of pearlite in Fig. 3. It is found that a linear relationship holds between VP and ε, meaning that the broadening of FWHM shown in Fig. 2 corresponds to the increase of pearlite volume fraction. Therefore, the lattice strain of ferrite phase in ferrite-pearlite steels, εF+P, could be described by the addition rule given by the following equation.   

ε F+P = ε F (1- V P )+ ε P V P (3)
Here, εF and εP denote the lattice strains of ferrite phase in single-structured ferritic and pearlitic steels, and these values under fully-normalized condition are found to be approximately 2.0×10−4 and 14×10−4, respectively.
Fig. 2.

X-ray diffraction peaks reflected from {110} ferrite in steels.

Fig. 3.

Relation between lattice strain of ferrite phase and volume fraction of pearlite.

The lattice strains (εP) of ferrite phase in SK85 (filled circle) and hypereutectoid steel (unfilled square) with different interlamellar spacing (L) are plotted as a function of the inverse of L in Fig. 4. In spite of the fact that all of the specimens have pearlite single structure, the εP markedly changes depending on L, which yields to the following equation.   

ε P =2.0× 10 -4 + 2.4× 10 -4 L (4)
The left endpoint of the linear line corresponds to the pearlite with infinite interlamellar spacing, namely, ferrite single phase steel, and thus, the constant term of Eq. (4) was fixed at the value of εF of high purity iron. Then, the Eq. (4) was obtained by the least-squares fitting using other data. Although there are some scattering of data points, this results reveals that the lattice strain of ferrite phase is increased due to the existence of cementite phase. Now considering that the area of ferrite/pearlite interface per unit volume can be approximated at 2/L,16) the linear relationship between εP and 1/L indicates that the elastic strain has been generated owing to the misfit of ferrite/cementite interface. Although the degree of misfit may be influenced by the partitioning of alloying elements between ferrite and cementite depending on the chemical composition of the steels, the identical line obtained in Fig. 4 demonstrates that the εP was dependent on only L in the case of commercial low alloy steels.
Fig. 4.

Effect of lamellar spacing on lattice strain of ferrite phase in pearlite steels.

As a result, inserting Eq. (4) into Eq. (3) gives a following equation.   

ε F+P =2.0× 10 -4 + 2.4× 10 -4 L V P (5)
On the other hand, TEM observation for all specimens used in this study revealed that the dislocation density of ferrite phase in pearlite was very low similarly to annealed ferritic steel, though some dislocations existed near the ferrite/cementite interface. In addition, clear interference fringes derived from the elastic strain was also observed. Therefore, we can conclude the second term of Eq. (5) mainly comes from the elastic strain existing in pearlite.

4. Conclusions

In order to quantify the dislocation density of ferrite-pearlite steel correctly, the effect of pearlite structure on the lattice strain in ferrite estimated by the Williamson-Hall method was investigated using normalized carbon steels with different volume fraction of pearlite and a hypereutectoid steel with different interlamellar spacing of cementite. The following results were obtained:

(1) The lattice strain of the ferrite phase in ferrite-pearlite steel is monotonically increased in proportion to the volume fraction of pearlite (Vp).

(2) The lattice strain of the ferrite phase within the pearlite structure increased in proportion to inverse of interlamellar spacing (L), which is due to the lattice misfit between ferrite and cementite.

(3) The lattice strain of the ferrite phase in ferrite-pearlite steel (εF+P) is described as a function of them, yielding to the following equation.   

ε F+P =2.0× 10 -4 + 2.4× 10 -4 L V p

Acknowledgment

We wish to tank Mr. S. Ueda of Nippon Steel & Sumitomo Metal Co. for the provision of steel used in this study.

References
 
© 2015 by The Iron and Steel Institute of Japan
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